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Permutation and Combination Worksheet for Olympiad

Maths Olympiad topic 22: Counting and arrangements · Set 201 · 40 questions
TalentJR

How to solve it (Multiply the choices): Multiplication principle: a ways for the first choice and b ways for the next give a × b ways together. n different letters in a row: n × (n − 1) × … × 2 × 1 arrangements. Handshakes, matches or teams of 2 from n (order does not matter): n × (n − 1) ÷ 2. Captain and vice-captain (order matters): n × (n − 1).

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  1. 1.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 132 (b) 66 (c) 144 (d) 24
  2. 2.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 56 (b) 11 (c) 28 (d) 32
  3. 3.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 70 (b) 42 (c) 35 (d) 12
  4. 4.There are 3 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 15 (b) 12 (c) 24 (d) 7
  5. 5.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 49 (c) 21 (d) 28
  6. 6.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 24 (d) 16
  7. 7.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 121 (c) 110 (d) 55
  8. 8.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 12 (c) 3 (d) 9
  9. 9.There are 6 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 9 (c) 36 (d) 24
  10. 10.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 144 (b) 24 (c) 132 (d) 66
  11. 11.There are 6 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 36 (b) 11 (c) 30 (d) 60
  12. 12.8 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 80 (b) 13 (c) 40 (d) 48
  13. 13.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 84 (b) 49 (c) 13 (d) 42
  14. 14.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 225 (d) 105
  15. 15.4 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 12 (b) 7 (c) 24 (d) 16
  16. 16.6 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 42 (b) 84 (c) 48 (d) 13
  17. 17.There are 7 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 14 (b) 21 (c) 9 (d) 28
  18. 18.There are 4 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 28 (b) 32 (c) 11 (d) 56
  19. 19.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 45 (c) 100 (d) 90
  20. 20.7 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 70 (b) 42 (c) 12 (d) 35
  21. 21.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 36 (c) 18 (d) 72
  22. 22.There are 6 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 18 (c) 24 (d) 8
  23. 23.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 28 (c) 56 (d) 64
  24. 24.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 12 (c) 30 (d) 36
  25. 25.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 91 (b) 169 (c) 78 (d) 156
  26. 26.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 32 (c) 16 (d) 8
  27. 27.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 81 (c) 72 (d) 18
  28. 28.There are 3 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 18 (c) 6 (d) 9
  29. 29.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 196 (c) 91 (d) 105
  30. 30.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 21 (d) 42
  31. 31.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 10 (c) 20 (d) 25
  32. 32.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 64 (c) 28 (d) 56
  33. 33.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 55 (c) 121 (d) 22
  34. 34.There are 4 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 24 (c) 10 (d) 28
  35. 35.In a league, 12 teams each play every other team once. How many matches are played? (a) 144 (b) 132 (c) 66 (d) 78
  36. 36.There are 5 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 15 (b) 20 (c) 30 (d) 8
  37. 37.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 20 (c) 15 (d) 8
  38. 38.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 35 (b) 40 (c) 12 (d) 70
  39. 39.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 21 (c) 49 (d) 42
  40. 40.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 132 (c) 144 (d) 78

Answer key

  1. 132
  2. 28
  3. 35
  4. 12
  5. 21
  6. 24
  7. 55
  8. 6
  9. 18
  10. 66
  11. 30
  12. 40
  13. 42
  14. 105
  15. 12
  16. 42
  17. 14
  18. 28
  19. 45
  20. 35
  21. 36
  22. 12
  23. 28
  24. 15
  25. 78
  26. 16
  27. 72
  28. 9
  29. 91
  30. 21
  31. 20
  32. 28
  33. 55
  34. 24
  35. 66
  36. 15
  37. 15
  38. 35
  39. 42
  40. 66

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